On the communication complexity of sparse set disjointness and exists-equal problems

In this paper we study the two player randomized communication complexity of the sparse set disjointness and the exists-equal problems and give matching lower and upper bounds (up to constant factors) for any number of rounds for both of these problems. In the sparse set disjointness problem, each player receives a k-subset of [m] and the goal is to determine whether the sets intersect. For this problem, we give a protocol that communicates a total of O(k\log^{(r)}k) bits over r rounds and errs with very small probability. Here we can take r=\log^{*}k to obtain a O(k) total communication \log^{*}k-round protocol with exponentially small error probability, improving on the O(k)-bits O(\log k)-round constant error probability protocol of Hastad and Wigderson from 1997. In the exist-equal problem, the players receive vectors x,y\in [t]^n and the goal is to determine whether there exists a coordinate i such that x_i=y_i. Namely, the exists-equal problem is the OR of n equality problems. Observe that exists-equal is an instance of sparse set disjointness with k=n, hence the protocol above applies here as well, giving an O(n\log^{(r)}n) upper bound. Our main technical contribution in this paper is a matching lower bound: we show that when t=\Omega(n), any r-round randomized protocol for the exists-equal problem with error probability at most 1/3 should have a message of size \Omega(n\log^{(r)}n). Our lower bound holds even for super-constant r <= \log^*n, showing that any O(n) bits exists-equal protocol should have \log^*n - O(1) rounds

Tight bounds for data stream algorithms and communication problems

In this thesis, we give efficient algorithms and near-tight lower bounds for the following problems in the streaming model. Improving on the works of Monemizadeh and Woodruff from SODA\u2710 and Andoni, Krauthgamer and Onak from FOCS\u2711, we give $L_p$-samplers requiring $O(epsilon^{-p}log^2n)$ space for $pin(1,2)$. Our algorithm also works for $pin[0,1]$, taking $tilde{O}(epsilon^{-1}log^2n)$ space. As an application of our sampler, we give an $O(log^2n)$ space algorithm for finding duplicates in data streams, improving the algorithms of Gopalan and Radhakrishnan from SODA\u2709. Given a stream that consists of a pattern of length $m$ and a text of length $n$, the pattern matching problem is to output all occurrences of the pattern. Improving on the results of Porat and Porat from FOCS\u2709, we give a $O(log{}nlog{}m)$ space algorithm that works entirely in the streaming model. Finally we show several near-tight lower bounds for the above problems through new results in communication complexity

Settling the complexity of the k-disjointness and the k-Hamming distance problems

Thesis (Ph.D.)--University of Washington, 2019Suppose that two parties, traditionally called Alice and Bob, are given respectively the inputs $x\in\mathcal{X}$ and $y\in\mathcal{Y}$ to a function $f\colon\mathcal{X}\times\mathcal{Y}\to\mathcal{Z}$ and are required to compute $f(x,y)$. Since each party only has one part of the input, they can compute $f(x,y)$ only if some communication takes place between them. The communication complexity of a given function is the minimum amount of communication (in bits) needed to evaluate it on any input with high probability. We study the communication complexity of two related problems, the $k$-Hamming distance and $k$-disjointness and give tight bounds to both of these problems: The $r$-round communication complexity of the $k$-disjointness problem is $\Theta(k\log^{(r)}k)$, whereas a tight $\Omega(k\log k)$ bound holds for the $k$-Hamming distance problem for any number of rounds. The lower bound direction of our first result is obtained by proving a {\em super-sum} result on computing the OR of $n$ equality problems, which is the first of its kind. Using our second bound, we settle the complexity of various property testing problems such as $k$-linearity, which was open since 2002 or earlier. Our lower bounds are obtained via information theoretic arguments and along the way we resolve a question conjectured by Erdős and Simonovits in 1982, which incidentally was studied even earlier by Blakley and Dixon in 1966

The rate of nasal carriage of Staphylococcus aureus and oxacillin resistance in our hospital

In this study, the rate of nasal carriage of S.aureus in hospital staff and oxacillin resistance in S.aureus ln strains were investigated. Conventional methods were used for the isolation and susceptibility. From 300 nasal swabs cultured, 100 (33.3%) S.aureus strains were isolated and 9 (9 %) of them were found to be oxacillin resistant. The isolates of S.aureus were found to be resistant to penicillin, ampicillin - sulbactam, cefazolin, clindamycin, eritromycin, tetracycline, gentamicin, trimethoprim-sulfamethoxazole, rifampin, ciprofloxacin, norfloxacin, ceftriaxone, imipenem and mupirocin in the rates of 93%, 5%, 7%, 9%, 11%, 20%, 6%, 5%, 4%, 1%, 3%, 2%, 1%, 2%, respectively. All the strains were found to be sensitive to vancomycin and teicoplanin. These results showed that oxacillin resistance is not an important problem in our hospital staff: However surveys should continue and precautions should be taken

The prevalence of enterotoxin and antibiotic resistance genes in clinical and intestinal Bacteroides fragilis group isolates in Turkey

This study was conducted to measure the antibiotic susceptibilities, corresponding gene contents, and the enterotoxin gene bft, in 50 Bacteroides fragilis group isolates, 25 of which were clinical and 25 intestinal. The resistance rates to amoxicillin/clavulanic acid, imipenem and metronidazole were low; ampicillin and tetracyclin resistance was high; clindamycin resistance and ermF gene presence was also high. Regarding phenotypical bacterial resistance and the presence of resistance genes, there was not statistically significant difference between clinical and intestinal isolates and bft positive and negative isolates. (C) 2015 Elsevier Ltd. All rights reserved

Intensive care experiences of intern nurse students: A qualitative study

Objectives: This study aimed to describe the experiences of nursing interns in the intensive care unit (ICU). Design: This study was a descriptive qualitative research. Settings, participants, methods: The study data were collected via focus group interviews of 25 nursing interns in the two different ICUs of a university hospital who had volunteered to participate in the study. There were four focus group interviews in all, one for each of four different groups of nursing interns. The semi-structured interview form was used in the study. Results: Seven themes emerged in the study: fear, awareness of nurses' roles, finding opportunities for selfimprovement, difficulty in caregiving, difficulty in communicating with the patients and the care team, experiencing ambivalent feelings related to death, and adaptation to the clinical environment. Conclusions: Doing one's internship in the ICU was evaluated by the nursing interns in this study as a beneficial practice despite the difficulties involved in it. It is recommended, that intensive-care practices be included in the undergraduate education program for nurses and that appropriate guidance and monitoring be given to the nursing interns in ICUs